Let T be the line passing through the points P(−2,7) and Q(2,−5) .Let F1 be the set of all pairs of circles (S1,S2) such that T is tangents to S1 at P and tangent to S2 at Q, and also such that S1 and S2 touch each other at a point, say, M. Let E1 be the set representing the locus of M as the pair (S1,S2) varies in F1. Let the set of all straight line segments joining a pair of distinct points of E1 and passing through the point R(1, 1) be F2.Let F2 be the set of the mid-points of the line segments in the set F2.Then, which of the following statements(s) is (are) TRUE?[JEE Adv 2018 P2]

Question

Let T be the line passing through the points P(−2,7) and Q(2,−5) .Let F1 be the set of all pairs of circles (S1,S2) such that T is tangents to S1 at P and tangent to S2 at Q, and also such that S1 and S2 touch each other at a point, say, M. Let E1 be the set representing the locus of M as the pair (S1,S2) varies in F1. Let the set of all straight line segments joining a pair of distinct points of E1 and passing through the point R(1, 1) be F2.Let F2 be the set of the mid-points of the line segments in the set F2.Then, which of the following statements(s) is (are) TRUE?

[JEE Adv 2018 P2]

Accepted Answer

Correct Answer is : The point (0,32) does NOT lie in E1

Answer

The point (−2,7) lies in E1

Answer

The point (

4

5

,

7

5

) does NOT lie in E2

Answer

The point (

1

2

,1) lies in E2

Answer

The point (0,

3

2

) does NOT lie in E1

JEE Advanced 2018 Paper 2

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